{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random    # 随机策略时用到\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(0,20,0.2)\n",
    "y_greedy = 0.4 * x\n",
    "y_e_greedy = 0.3 * x\n",
    "y_decay = 2 * np.log10(x+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,6))#subplots(nrows=1, ncols=2, figsize=(12,8))\n",
    "#fig.suptitle(r'3D surface of $J(w_1,w_2)$ and gradient descent')\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "\n",
    "\n",
    "ax.plot(x, y_greedy, color=\"green\")\n",
    "ax.plot(x, y_e_greedy, color = \"red\")\n",
    "ax.plot(x, y_decay, color = \"black\")\n",
    "\n",
    "ax.set_xlabel(xlabel='time-steps', fontsize=15)\n",
    "ax.set_ylabel(ylabel='total reget', fontsize =15)\n",
    "ax.set_title(\"\")\n",
    "plt.yticks([])\n",
    "\n",
    "greedy = ax.text(7.2, 3.8, r'$greedy$', fontsize=15, color=\"green\")\n",
    "greedy = ax.text(12.5, 3.3, r'$\\epsilon-greedy$', fontsize=15, color=\"red\")\n",
    "greedy = ax.text(12.5, 1.7, r'$decaying\\ \\epsilon-greedy$', fontsize=15)\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gaussian_density(x, mu = 0, sigma = 1 ):\n",
    "    expo = -1 * np.power((x-mu),2)/(2*np.power(sigma,2))\n",
    "    return np.power(np.e,expo)/(np.sqrt(2*np.pi)*sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(-1.98, 5.98, 0.04)\n",
    "y = gaussian_density(x, mu=2.2, sigma = 0.3)\n",
    "y1 = gaussian_density(x, mu=1.6, sigma = 0.8)\n",
    "y2 = gaussian_density(x, mu=1.2, sigma = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,6))#subplots(nrows=1, ncols=2, figsize=(12,8))\n",
    "#fig.suptitle(r'3D surface of $J(w_1,w_2)$ and gradient descent')\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "#ax.grid()\n",
    "\n",
    "# 隐藏上边和右边\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.spines['right'].set_color('none')\n",
    "# 移动另外连个轴\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.spines['bottom'].set_position(('data', 0))\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "ax.spines['left'].set_position(('data', 0))\n",
    "\n",
    "plt.yticks([])\n",
    "plt.xticks([-1,1,2,3,4,5])\n",
    "ax.plot(x, y, color=\"green\")\n",
    "ax.plot(x, y1, color = \"red\")\n",
    "ax.plot(x, y2, color = \"blue\")\n",
    "\n",
    "ax.set_xlabel(xlabel='Q', fontsize=15)\n",
    "ax.set_ylabel(ylabel='p(Q)', fontsize =15)\n",
    "ax.set_title(\"\")\n",
    "\n",
    "\n",
    "qa1 = ax.text(0.1, 0.25, r'$Q(a_1)$', fontsize=15, color=\"blue\")\n",
    "qa2 = ax.text(1.2, 0.55, r'$Q(a_2)$', fontsize=15, color=\"red\")\n",
    "qa3 = ax.text(2.6, 0.8, r'$Q(a_3)$', fontsize=15, color=\"green\")\n",
    "\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
